Suppose the line y=5x-4 is tangent to the curve y=f(x) when x=3. If newton's method is used to locate a root of the equation f(x)=0 and the initial approximation is x1=3, find the second approximation x2.
can someone help me with this one? thanks
Suppose the line y=5x-4 is tangent to the curve y=f(x) when x=3. If newton's method is used to locate a root of the equation f(x)=0 and the initial approximation is x1=3, find the second approximation x2.
can someone help me with this one? thanks
The equation is not linear, at least you are not told that it is, only that $\displaystyle y=5x-4$ is a tangent to $\displaystyle y=f(x)$ at $\displaystyle x=3$. But being a tangent means that you can use it to find the derivative at the point as well as the functional value. Hence that $\displaystyle y=5x-4$ is a tangent allows you to perform one step of Newton's method.
Now you nothing of the true function value at $\displaystyle x=0.8$ nor its derivative so with the given information no further step is possible, but this would only be the exact root if $\displaystyle f(x)=5x-4$, which we are not told.
CB